Answer:
a = 950
s = 550
Step-by-step explanation:
Let a = the number of adult tickets purchased.
Let s = the number of student tickets purchased.
Therefore,
[tex]a + s = 1500 \implies \: s = 1500 - a...(1) \\ 2a + 3.5s = 3825...(2) \\ plugging \: s = 1500 - a \: in \: equation \: (2) \\ 2a + 3.5(1500 - a) = 3825 \\ 2a + 5250 - 3.5a = 3825 \\ 5250 - 1.5a = 3825 \\ 5250 - 3825 = 1.5a \\ 1425 = 1.5a \\ a = \frac{1425}{1.5} \\ \huge \red{ \boxed{ a = 950}} \\\implies s = 1500 - 950 \\ \huge \purple{ \boxed{s = 550}}[/tex]
So,
Number of adult tickets sold = 950
Number of students tickets sold = 550
Solve the following
a) 2(x+3)= x-4
b) 4(5x-2)= 2(9x+3)
A package of books weighs 72 ounces. What is the weight of the package in pounds?
Answer: 4.5 pounds
Explanation: To convert 72 ounces into pounds, we use the conversion factor for ounces and pounds which is 16 ounces = 1 pound.
Next, notice that we're going from a smaller unit, ounces, to a larger unit, pounds and when we go from a smaller unit to a larger unit, we divide. So here, we divide 72 by the conversion factor, 16, to get 4.5.
So 72 ounces equals 4.5 pounds.
A cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is 7pi/12. The graph of the function does not show a phase shift. What is the equation of the cosine function described?
Fill in the blanks using values from this list: -20, -11, -9, -2, 2, 9, 11, 20, 7pi/12,12pi/7,7/24,24/7
f(x)=___cos(_____x)______
We have been given that a cosine function is a reflection of its parent function over the x-axis. The amplitude of the function is 11, the vertical shift is 9 units down, and the period of the function is [tex]\frac{7\pi}{12}[/tex]. The graph of the function does not show a phase shift. We are asked to write the equation of our function.
We know that general form a cosine function is [tex]y=A\cos(b(x-c))-d[/tex], where,
A = Amplitude,
[tex]\frac{2\pi}{b}[/tex] = Period,
c = Horizontal shift,
d = Vertical shift.
The equation of parent cosine function is [tex]y=\cos(x)[/tex]. Since function is reflected about x-axis, so our function will be [tex]y=-\cos(x)[/tex].
Let us find the value of b.
[tex]\frac{2\pi}{b}=\frac{7\pi}{12}[/tex]
[tex]7\pi\cdot b=24\pi[/tex]
[tex]\frac{7\pi\cdot b}{7\pi}=\frac{24\pi}{7\pi}[/tex]
[tex]b=\frac{24}{7}[/tex]
Upon substituting our given values in general cosine function, we will get:
[tex]f(x)=-11\cos(\frac{24}{7}x)-9[/tex]
Therefore, our required function would be [tex]f(x)=-11\cos(\frac{24}{7}x)-9[/tex].
y=2x+3
y=−3x+3
find slope and y-intercept
Answer:
y = 2x + 3 → Gradient / slope = 2 → Y - intercept = 3
y = -3x + 3 → Gradient / slope = -3 → Y - intercept = 3
Step-by-step explanation:
y = mx + c
This is the standard way an equation of a line is written. The 'm' of the line is the slope/gradient and the 'c' is the y - intercept. You can find the x-intercept by making y = 0. When the questions asks you to find the gradient you should never put 'x' after it only the number so
y = 2x + 3
Gradient / slope = 2
Y - intercept = 3
y = -3x + 3
Gradient / slope = -3
Y - intercept = 3
h(x) = 4x - 3
Given ƒ(x) and h(x), ƒ(x) has the greater value when x = 2.
a. true
b. false
consider the graph of the function y=1/4x2-3x-40. what are the roots of the function?
Answer: the roots are x = 20 and x = -8
Step-by-step explanation:
We have the function
y = (1/4)x^2 - 3x - 40
We want to find the roots, that are the points in where y(x) = 0
For a quadratic equation of the form:
y = a*x^2 + bx + c the roots are:
[tex]x = \frac{-b +-\sqrt{b^2 -4*a*c} }{2*a}[/tex]
in this case we have:
[tex]x = \frac{3 +-\sqrt{3^2 +4*(1/4)*40} }{2*(1/4)}= \frac{3 +-7}{(1/2)}[/tex]
So the two roots are:
x = 2*(3 + 7) = 20
x = 2*(3 - 7) = -8
Screen Shot 2020-05-18 at 9.51.50 AM
Screen Shot 2020-05-18 at 9.57.43 AM
Answer:
there is nothing there
Step-by-step explanation:
literally
Answe
Step-by-step explanation:
Imani sells shirts packed in boxes that are each 15in. x 10in. x 2in. Imani stacked 3 boxes and wrapped them with one piece of paper. How much paper did she use, not including overlap?
Answer:
She used 600 square inches of paper.
Step-by-step explanation:
Since the box are 15 in x 10 in x 2 in and are stacked on top of each other, they form a bigger rectangular prism with 15 in x 10 in x 6 in. In order to calculate how much paper she used, we need to calculate the surface area of this prism, this is done by using the following formulla:
surface area = 2*width*length + 2*width*height + 2*length*height
surface area = 2*15*10 + 2*15*6 + 2*10*6 = 300 + 180 + 120
surface area = 600 in².
She used 600 square inches of paper.
Joel has a goal to practice is clarinet for 4 1/2 hours per week the list below shows the number of hours Chihuahuas practice so far this week Monday 1 1/2 hours Wednesday 11
Complete question:
Joel has a goal to practice his clarinet for 4 1/2 per week. The list below shows the number of hours Joel has a practiced so far for the week. Monday 1 1/2 hours Wednesday 1 1/4 hours Thursday 1 hour How many more hours does he need to practice this week to meet his goal
Answer: 3/4 hours
Step-by-step explanation:
Target hours = 4 1/2 hours = 9/2 hours
Number of hours so far :
(1 1/2 + 1 1/4 + 1) = (3/2 + 5/4 + 1) hours
Total so far :
L. C. M of denominator = 4
(6 + 5 + 4) /4 = 15/4
Number of hours left to meet his target equals :
Target hours - total so far
( 9/2 - 15/4)
L. C. M of denominator = 4
(18 - 15) / 4 = 3/4 hours
.
s= ut + 1/2 at x2
u=10
a=-2
t=1/2
work out the value of s
Answer:
s = 4 3/4.
Step-by-step explanation:
The formula is s = ut + 1/2 at^2
so s = 10^1/2 + 1/2 * -2 * (1/2)^2
s = 5 - 1/4
= 4 3/4.
(100 POINTS):( You will be reported if you provide an inapplicable answer)
use this function to answer the questions
f(x) = 2x^2 − 5x + 3
-Find The X intercepts of the graph
-Is the Vertex Going To Be Minimum Or Maximum? (I may be able to figure this one out)
-What is The Coordinates Of The Vertex?
-What Would You Do To Graph f(x)?
Please Explain because I want to understand it! mainly just need help with the first and then I may be able to take it from there.
Answer:
x-intercept(s):
(1,0),(3/2,0)
y-intercept(s): (0,3)
Use the formula
x=−b/2a to find the maximum and minimum.
Ans;(5/4,−1/8)
Coordinates Of The Vertex
(5/4,−1/8)
Zero (roots)
x=1,3/2
Step-by-step explanation:
Easy 6th grade question please mark Brainliest and give extra points
Question The The point (0,1)
(
0
,
1
)
is reflected over the x- axis. What are the coordinates of the resulting point?
Answer:
it would be the same since its ON the x-axis ( the point does not change)
Step-by-step explanation:
A triangle has a base length of (2x - 4) units and a height of (x + 5) units. Write and solve a quadratic equation to determine what value of x gives the triangle an area of 44 square units
Answer:
x = -9
x = 6 BUT IT DOES NOT WORK WHEN YOU PLUG IT BACK IN
Step-by-step explanation:
Triangle area = 1/2 bh
The area is given (44)
base = 2x-4
height = x+5
44 = 1/2 (2x-4) (x+5)
Distribute
44 = 1/2 (2x^2 + 10x - 4x - 20)
44 = 1/2 (2x^2 + 6x - 20)
Take out a 2
44 = 2 * 1/2 (x^2 + 3x - 10)
44 = x^2 + 3x - 10
Subtract 44
0 = x^2 + 3x - 54
Factor the way you like and you should get
(x + 9) (x - 6)
x = -9
x = 6
If you plug them in only the -9 works.
44 = 1/2 (-22) (-4)
Answer:
x=6
Step-by-step explanation:
[tex]\frac{1}{2} (2x-4)(x+5)=44\\(x-2)(x+5)=44[/tex]
[tex]x^{2} -2x+5x-10=44\\x^{2} +3x-54=0[/tex]
[tex]x^{2} +9x-6x-54=0\\x(x+9)-6(x+9)=0\\(x+9)(x-6)=0\\x=-9(rejected),6[/tex]
side is 2×6-4=8 units
height=x+5=6+5=11 units
x=-9 is rejected because it gives negative side and negative height.
Help with this question please!!
Answer:
Width = 160
Length = 110
Step-by-step explanation:
Perimeter is the sum of all the sides
They tell you that the length is 50 m shorter than the width
so L = W - 50
W = W
540 = W + W + W-50 + W-50
540 = 2W + 2(W-50)
540 = 2W + 2W - 100
540 = 4W - 100
640 = 4W
W = 160
L = 160 - 50
L = 110
Answer:
Length: 110 m
Width: 160 m
Step-by-step explanation:
The formula for perimeter of a rectangle is P = 2L + 2W.
We can write the length in terms of width if width is w:
Length: w - 50
Width: w
Plug the values into the formula.
540 = 2(w - 50) + 2w
540 = 2w - 100 + 2w
540 = 4w - 100
640 = 4w
w = 160
find length by subtracting 50 from the width
160-50=110
Therefore, the length is 110 and the width is 160.
Please help ASAP! I will mark Brainliest! Please answer CORRECTLY! No guessing! Show your work!
Answer: Increased A.
Step-by-step explanation:
HELPP MEE FASTT I HAVE LESS THAN 10 MIN
Farrah borrowed $155 from her brother. She has already paid back $15. She plans to pay back $35 each month until the debt is paid off.
Which describes the number of months it will take to pay off the debt? Select three options.
x + 15 + 35 = 155
35 x + 15 = 155
35 x = 155 minus 15
It will take 8 months to pay off the debt.
It will take 4 months to pay off the debt.
Answer:
35x + 15 = 155
35x = 155 minus 15
it will take 4 months to pay off the debt.
Hope this helps. Mark brainliest please!
Answer:
35x + 15 = 155
35x = 155 - 15
It will take 4 months to pay off debt
Step-by-step explanation:
Its mental so idk but trust me <3
Mrs. Juarez graded ten English papers and recorded the scores. 92, 95, 100, 62, 88, 90, 100, 96, 89, 98 Which statements are true? Check all that apply.
Answer:
A, B, E
explanation:
Answer:
A: The range of scores is 38.
B: Without the outlier, the range of scores would be 12.
C: The outlier impacts the range more than it impacts the interquartile range.
D: The interquartile range is 9.
F: Without the outlier, the interquartile range would be 9.5.
Step-by-step explanation:
edg2020
select the correct answer you're getting two side lengths of 10 cm and 8 centimeters the angle between the sides measure 40° how many triangles can you construct using his measurements? WILL GIVE BRAINLIEST PLZ HELP
Answer:
Step-by-step explanation:
16 triangles
the radius of a circle with a circumstance of 28 pie into units
Answer:
The radius is 14
Step-by-step explanation:
The circumference of the circle is 28 pi
C = 2* pi *r where r is the radius
28 pi = 2 pi *r
Divide each side by 2 pi
28 pi/2pi = 2 pi *r/2pi
14 = r
Please help will mark brainliest!!!
How would you describe the graph of the function at interval 3? Select all that apply.
image below
Answer:
B and E
Step-by-step explanation:
In the graph, the altitude represents Y axis while time represents the X axis. we can see that at interval 1 the function is dramatically decreasing. At Interval 2 the function is constant. At interval 3 the function is increasing but I can't say definitively if the slope is positive or negative. Hope this helped!
WILL MARK THE BRAINLIEST!!!! What is a function?
Answer:
In mathematics, a function is a binary relation over two sets that associates to every element of the first set exactly one element of the second set. Typical examples are functions from integers to integers or from the real numbers to real numbers.
Step-by-step explanation:
3. This table shows a linear relationship between the amount of water in a tank and
time.
time (minutes) water (gallons)
0 T| 30 G
5 T| 20 G
10T| 10 G
Which of these statements is true?
OD
A.The water in the tank is increasing at a rate of 2 gallons per minute.
B.The water in the tank is increasing at a rate of 10 gallons per minute.
C.The water in the tank is decreasing at a rate of 2 gallons per minute.
D.The water in the tank is decreasing at a rate of 10 gallons per minute.
OL
Answer:
c because 10gallons per min is to much
Step-by-step explanation:
The water in the tank is decreasing at a rate of 2 gallons per minute. Therefore, option C is the correct answer.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
The given table shows a linear relationship between the amount of water in a tank and time.
From the table we have (0, 30), (5, 20) and (10, 10).
Now, slope m=(20-30)/(5-0)
m= -2
Substitute (x, y)=(0, 30) and m=-2 in y=mx+c, we get
30=-10(0)+c
c=30
Now equation is y=-2x+30
Here, the water in the tank is decreasing at a rate of 2 gallons per minute.
Therefore, option C is the correct answer.
To learn more about the equation of a line visit:
https://brainly.com/question/2564656.
#SPJ2
find out three rational numbers lying between 2/3 and 3/4
PLEASE HELP...... I NEED TO SUBMIT IT NOW......
Answer:
33/48, 34/48, 35/48
Step-by-step explanation:
2/3 is equal to 32/48 and 3/4 is equal to 36/48. The fractions in between them are all rational numbers. Hope this helped <3
Pls help with 9 and Tysm
Answer:
the last one
Step-by-step explanation:
a number used to multiply a variable
Can someone pls help me!!
The point-slope form of a line that has a slope of
and passes through the point (3, 0) is shown.
y -0 =3(2-3)
What is the equation in slope-intercept form?
A. y=1/4x-3
B. y=1/4x3/4
C. y=3/4x-1/4
D. y=1/4x-1/12
How many fourths are in 2 1/2?
Answer:
There are 10 fourths.
Step-by-step explanation:
There are four 1/4ths in 1. So 2.5 x 4 = 10.
Answer:
2 1/2 is the same as 5/2 which is the same as 10/4, so 10 is the answer :)
Step-by step solution
The ratio of cars to trucks passing the intersection of Reyes Adobe and TO Blvd is 7:2. If 108 vehicles pass this intersection, how many are cars?
Answer:
84 cars
Step-by-step explanation:
the the ratio is 7 to 2. There were 108 vehicles. 108/ 9=12
12 x 7= 84.... or at least that's how I think of it.
Is it possible to triangulate a quadrilateral and get more or fewer than two triangles? Determine whether this investigation verifies that the sum of the interior angles of a quadrilateral is always 360°.
Answer:
No.
Step-by-step explanation:
It’s not possible. No matter what type of quadrilateral it is, there will only be two triangles formed, verifying that the sum of the interior angles of a quadrilateral is always 360°.
It’s not possible to triangulate a quadrilateral and get more or fewer than two triangles. It is verifies that the sum of the interior angles of a quadrilateral is always 360°.
What is a quadrilateral?Any closed figure made by 4 line segments joined end to end in series is called a quadrilateral.
It’s not possible to triangulate a quadrilateral and get more or fewer than two triangles. No matter what type of quadrilateral it is, there will only be two triangles formed.
We know that The sum of internal angle of a quadrilateral is 360°.
The sum of angle in a triangle is 180°. By Adding the two triangle angle together, we will get the sum as 360°.
The Sum of the interior angle of a polygon = 180(n-2) .
It is verifies that the sum of the interior angles of a quadrilateral is always 360°.
Learn more about quadrilateral;
https://brainly.com/question/2477872
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Lucas built a composite solid by joining 12 identical blocks, with dimensions 4 inches by 5 inches by 7 inches, into three
ows of four as shown.
7 in.
5 in
4 in
What is the total surface area of the composite solid?
O 521 square inches
1,042 square inches
1,072 square inches
O 1.992 square inches
Answer:
1042 square inches is the total surface area of composite solid.
Step-by-step explanation:
It is clear from the image that the resulting composite solid is a cuboid.
whose sides are as follows:
Across the length there are 3 blocks along the side of 7 inches each.
Length = [tex]7 \times 3 = 21\ inch[/tex]
Width = 5 inch
Across the height there are 4 blocks along the side of 4 inches each.
Height = [tex]4 \times 4 = 16\ inch[/tex]
We know that total surface area of a cuboid is as follows:
[tex]\text{Total Surface Area = } 2 (l\times w+ w \times h+ h \times l)[/tex]
[tex]\Rightarrow 2 (21 \times 5 + 16 \times 21 + 16 \times 5 )\\\Rightarrow 2 (105 + 336+80)\\\Rightarrow 2 \times 521\\\Rightarrow 1024[/tex]
Hence, total surface area = 1024 square inches
Step-by-step explanation: i got it right
